Methods and apparatuses for trap-door loading

ABSTRACT

Aspects of the present disclosure may include a method and/or a system for trap-door loading including pumping at least one qubit ion from a first manifold of a first plurality of manifolds to a second manifold of the first plurality of manifolds, drive the at least one qubit ion via a partial clock transition from the second manifold of the first plurality of manifolds to a third manifold of a second plurality of manifolds, applying one or more Raman pulses to transfer the at least one qubit ion from the third manifold of the second plurality of manifolds to a fourth manifold of the second plurality of manifolds, flushing the at least one qubit ion using a high-fidelity pumping back to the first plurality of manifolds, and illuminating the first plurality of manifolds for verification.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to, and the benefit of, U.S. PatentProvisional Application No. 63/222,765, filed Jul. 16, 2021, and U.S.Patent Provisional Application No. 63/286,846, filed Dec. 7, 2021, theentire contents of each of which are hereby incorporated by reference.

TECHNICAL FIELD

Aspects of the present disclosure relate generally to quantuminformation processing (QIP) architectures, and more particularly, todual-space, single-species architecture for trapped-ion QIP.

BACKGROUND

Trapped atoms are one of the leading implementations for quantuminformation processing or quantum computing. Atomic-based qubits can beused as quantum memories, as quantum gates in quantum computers andsimulators, and can act as nodes for quantum communication networks.Qubits based on trapped atomic ions enjoy a rare combination ofattributes. For example, qubits based on trapped atomic ions have verygood coherence properties, can be prepared and measured with nearly 100%efficiency, and are readily entangled with each other by modulatingtheir Coulomb interaction with suitable external control fields such asoptical or microwave fields. These attributes make atomic-based qubitsattractive for extended quantum operations such as quantum computationsor quantum simulations.

It is therefore important to have architectures that take advantage ofatomic-based qubits, including architectures that support differenttypes of trapped-ion techniques.

SUMMARY

The following presents a simplified summary of one or more aspects toprovide a basic understanding of such aspects. This summary is not anextensive overview of all contemplated aspects and is intended toneither identify key or critical elements of all aspects nor delineatethe scope of any or all aspects. Its sole purpose is to present someconcepts of one or more aspects in a simplified form as a prelude to themore detailed description that is presented later.

Aspects of the present disclosure relate generally to systems andmethods for use in the implementation and/or operation of quantuminformation processing (QIP) systems, and more particularly, toimplement trap-door readout. Aspects of the present disclosure includespumping at least one ancilla ion from a first manifold to a secondmanifold via Raman transitions, and applying a global clock beam to theat least one ancilla ion to transfer the at least one ancilla ion fromthe second manifold to a third manifold.

Aspects of the present disclosure relate generally to systems andmethods for use in the implementation and/or operation of quantuminformation processing (QIP) systems, and more particularly, toimplement trap-door loading. Aspects of the present disclosure includespumping at least one qubit ion from a first manifold to a secondmanifold, drive the at least one qubit ion via a partial clocktransition to a third manifold, applying one or more Raman pulses totransfer the at least one qubit ion to a fourth manifold, flush the atleast one qubit ion using a high-fidelity pumping, and illuminating aplurality of manifolds for verification.

Aspects of the present disclosure may include a method and/or a systemfor trap-door loading including pumping at least one qubit ion from afirst manifold of a first plurality of manifolds to a second manifold ofthe first plurality of manifolds, drive the at least one qubit ion via apartial clock transition from the second manifold of the first pluralityof manifolds to a third manifold of a second plurality of manifolds,applying one or more Raman pulses to transfer the at least one qubit ionfrom the third manifold of the second plurality of manifolds to a fourthmanifold of the second plurality of manifolds, flushing the at least onequbit ion using a high-fidelity pumping back to the first plurality ofmanifolds, and illuminating the first plurality of manifolds forverification.

To the accomplishment of the foregoing and related ends, the one or moreaspects comprise the features hereinafter fully described andparticularly pointed out in the claims. The following description andthe annexed drawings set forth in detail certain illustrative featuresof the one or more aspects. These features are indicative, however, ofbut a few of the various ways in which the principles of various aspectsmay be employed, and this description is intended to include all suchaspects and their equivalents.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosed aspects will hereinafter be described in conjunction withthe appended drawings, provided to illustrate and not to limit thedisclosed aspects, wherein like designations denote like elements, andin which:

FIG. 1 illustrates an example of a dual-space, single speciesimplementation in 133Ba+ in connection with aspects of this disclosure.

FIG. 2 illustrates a first class of features related to qubits pluscoolant/calibration ions in connection with aspects of this disclosure.

FIG. 3 illustrates a second class of features related to qubits plusancillas plus coolant ions in connection with aspects of thisdisclosure.

FIG. 4 illustrates an example of sympathetic cooling/calibration inconnection with aspects of this disclosure.

FIG. 5 illustrates an example of an alternative sympatheticcooling/calibration in connection with aspects of this disclosure.

FIG. 6 illustrates an example of an ancilla readout in connection withaspects of this disclosure.

FIG. 7 illustrates an example of mid-algorithm calibration via ancillareadout in connection with aspects of this disclosure.

FIGS. 8 and 9 illustrate an example of a REG and distribution viaancilla in connection with aspects of this disclosure.

FIG. 10 illustrates an example of m-type Raman gates in connection withaspects of this disclosure.

FIG. 11 illustrates a first class of features with m-type Raman relatedto qubits plus coolant/calibration ions in connection with aspects ofthis disclosure.

FIG. 12 illustrates a second class of features with m-type Raman relatedto qubits plus ancillas plus coolant ions in connection with aspects ofthis disclosure.

FIG. 13 illustrates a laser scheme for high-fidelity dual-spaceoperation in connection with aspects of this disclosure.

FIG. 14 illustrates an example of a quantum information processing (QIP)system in which a dual-space, single species architecture can beimplemented according to aspects of the present disclosure.

FIG. 15 illustrates an example of a computer device in which adual-space, single species architecture can be implemented for quantuminformation processing according to aspects of the present disclosure.

FIG. 16 illustrates an example of Ba-137 level structure with allowedtransitions between the clock states in accordance with aspects of thisdisclosure.

FIG. 17 illustrates an example of trap-door readout in accordance withaspects of this disclosure

FIG. 18 illustrates an example of trap-door loading in accordance withaspects of this disclosure.

FIG. 19 illustrates an example of a method for preparing barium 137 ionsaccording to aspects of the present disclosure.

DETAILED DESCRIPTION

The detailed description set forth below in connection with the appendeddrawings is intended as a description of various configurations and isnot intended to represent the only configurations in which the conceptsdescribed herein may be practiced. The detailed description includesspecific details for the purpose of providing a thorough understandingof various concepts. However, it will be apparent to those skilled inthe art that these concepts may be practiced without these specificdetails. In some instances, well known components are shown in blockdiagram form in order to avoid obscuring such concepts.

In general, dual-species trapped-ion quantum computing is consideredadvantageous for practical, high-fidelity systems. This approach can beused to mitigate decoherence of data and syndrome qubits duringsympathetic cooling in the middle of long algorithms and/or after iontransport, mid-algorithm qubit readout of a subset of the quantumprocessor, mid-algorithm remote entanglement generation (REG), andmid-algorithm calibration. This approach relies on having differentspecies with very different transition frequencies. These differencesneed to be large compared with transition linewidths and transitionrates.

But the use of dual-species in trapped-ion quantum computing can havesome challenges. For example, more lasers and optical beams are needed,chain (e.g., linear arrangement of ions) order matters both for ionaddressability and mode structure, and more complicated loading, andunintended chain reordering may cause some issues. Moreover, sympatheticcooling in mixed species chains (especially radial modes) can beinefficient, while shuttling and split/merge operations in mixed specieschains is challenging due to different pseudopotentials seen by ions ofdifferent mass. Mixed-species two-qubit (2q) gates (needed for REGdistribution) can have lower fidelity.

The Dual-Space Concept

The dual-space concept is described in connection with FIG. 1 . For thisapproach, there is the use of two Hilbert spaces in one ion species togain dual-species functionality. These spaces are naturally decoupledbut can be coupled through application of optical fields. Spaces eitherconsist of ground state or metastable state.

This approach is sometimes referred to as the “omg” or “OMG” conceptbecause it involves an optical qubit (i.e., o-type, shown as a circlewith vertical lines in FIG. 1 ) for high-fi measurement, a metastablequbit (i.e., m-type, shown as a circle with dots in FIG. 1 ) forprotected memory with low-field clock states, T1˜30 s, and a groundqubit (i.e., g-type, shown as a circle with horizontal lines in FIG. 1 )for processing, cooling, and remote entanglement generation. Thisapproach involves arrow quadrupole transitions for changing types:“Hilbert space shuttling” (HSS).

Sympathetic Cooling

In a trapped-ion quantum computer, the collective motional modes of achain of ions must be cooled to enable high-fidelity manipulation of theatomic qubits. However, during a calculation, electric field noise leadsto heating of these motional modes, which can degrade the system'sperformance over the course of the calculation. Additionally, to performa calculation that involves ions in multiple chains, the chains must beshuttled spatially during the calculation, which can also lead toheating of the motional modes. Sympathetic cooling is typically used tocool these motional modes during a calculation. This involves performingthe calculation using one set of “qubit” ions while simultaneouslyperforming laser-cooling operations on a separate set of “coolant” ions,which has the effect of cooling the collective motional modes of theentire chain. This has been demonstrated by using two separate elements(e.g., Yb and Ba) or two isotopes of the same element (e.g., Yb-171 andYb-172) for the qubit and coolant ions.

However, one problem is that the coupling of individual ions to thecollective motional modes depends on those ions' masses, and so ionsthat have different masses—as different elements or isotopes do—coupledifferently to the motional modes, degrading the effectiveness of thesympathetic cooling scheme. Further, the presence of ions with differentmasses complicates the design of quantum gates, which are highlysensitive to properties of the collective motional modes. A secondsignificant technical problem is that collision with background gasmolecules can cause the ions in the chain to reorder, scrambling thequbit and coolant ions and forcing the slow and costly operation ofeither re-ordering or rebuilding the chain. A third problem, for chainscomposed of two isotopes of the same element, is that the frequencies ofthe optical transitions involved in cooling the coolant ions aretypically close to those of the qubit ions, and so light that is emittedby the coolant ions can be absorbed by the qubit ions, degrading thecalculation.

There are some of the advantages to the approach described herein inconnection with sympathetic cooling. Because the qubit and coolant ionsare identical, the problems related to different masses and chainreordering are eliminated. Further, because all ions in the chain areidentical until they are assigned to be either qubit or coolant ions,the assignment can be determined dynamically for each calculation tooptimize the number and positions of coolant ions without reloading anew chain.

High-Fidelity Readout

At the end of a computation the states of all qubit ions must be readout optically. Generally, this is done by applying a global detectionlaser, which will cause ions that are in the “bright” state to fluorescebut not ions that are in the “dark” state. Because the bright and darkstates for a hyperfine qubit are generally part of the same manifold(i.e., the S_(1/2) states in ¹³³Ba⁺ or ¹⁷¹Yb), the transition(s)addressed by the detection laser must be chosen carefully to avoidexciting the ion out of the dark state, thereby leading to erroneousfluorescence, and also to avoid pumping the ion from the bright state tothe dark state, thereby leading to an erroneous lack of fluorescence.Often, the rates at which these errors occur are set by the intrinsicatomic properties of the ion, placing a fundamental limit on thefidelity with which the ion's state can be read out.

There are various advantages to the approach described herein inconnection with the read out. For example, these errors can be avoidedby transferring one of the qubit states into a separate manifold (i.e.,the D_(5/2) states in ¹³³Ba⁺), a process known as shelving. The ion canthen be illuminated in such a way so that all states in the originalmanifold fluoresce. Because the two manifolds are decoupled, the rate atwhich the dark state (the state that has been shelved) can be caused toerroneously fluoresce and the rate at which the bright state (the statethat has not been shelved) can erroneously stop fluorescing areextremely small. As a result, the readout fidelity can be made to beextremely high.

Mid-Circuit Calibration

The fidelity of a quantum computation is extremely sensitive to a widevariety of experimental factors, such as optical beam alignment, laserintensity at the ions, the strength of the confining potential thattraps the ions, the presence of stray electric fields, and many others.These factors are likely to drift or change over time, so calibrationsneed to be performed to account for this drift.

Because these calibrations require reading the states of the ions toextract information about these factors, they are typically performedbetween computations, during which it is forbidden to read the states ofthe qubit ions involved in the computation. However, this limits thespeed at which these calibrations can be performed, limiting thebandwidth of the calibration feedback.

Alternatively, calibrations can be performed during the computationusing ancilla ions that are not involved in the computation itself.However, because these calibration routines collect fluorescence fromthe ancilla ions to read out their states, it has formerly been requiredto use either a different atomic element or different isotope for theancilla ions so that this fluorescence does not disturb the states ofthe qubit ions that are involved in the computation. Consequently,various properties of the ancilla ions may be different from those ofthe qubit ions, which causes them to be influenced by these experimentalfactors in subtly different ways and may limit the predictive value ofancilla-based calibrations.

There are various advantages to the approach described herein inconnection with mid-circuit calibration. For example, the ancilla andqubit ions are identical, and the calibration routines are performed byprecisely the same techniques that are used to run the computation.Therefore, the calibration results do not need to be adjusted to accountfor physical differences between the calibration routines run on theancilla ions and the computation run on the qubit ions.

Mid-Circuit Partial Readout

Many quantum algorithms or circuits involve measuring a fraction of thequbits mid-circuit while requiring that the unmeasured fraction remaincoherent. Such mid-circuit measurement can be a critical component ofquantum error correction (QEC). In QEC, ancilla qubits, which areentangled with data qubits, are measured to herald and identify errorsin the data qubits. The error in the data qubits can then be correctedby subsequent quantum operations, but this only works if the quantuminformation in the data qubits is not destroyed during the measurementof the ancillas. This presents a challenge for single-speciestrapped-ion-qubit systems because measurement of ancillas typicallyrequires the scattering of many photons from a readout laser, and thesephotons can be reabsorbed by nearby data ions causing their quantuminformation to be lost. One standard approach to solve this problem isto move the ancilla ions far away from the data ions after they areentangled with them, but before (and during) measurement. However, thisdynamic, mid-circuit reconfiguration of ion-qubit positions can beimpractical or undesirable in many situations. The use of dual-speciestrapped-ion systems, where ancillas and data ions are different species,also mitigates this problem and allows ions to stay close to oneanother. However, the disadvantages of dual species operation havealready been elucidated earlier. In this mid-circuit partial readoutprotocol for QEC, dual-species entangling (two-qubit) gates may berequired, which may typically have a fidelity that is not as good asthat of single-species entangling gates.

There are various advantages to the approach described herein inconnection with mid-circuit partial readout. For example, data qubitscan be stored in the m-type space while ancillas are measured. Thisprotects the quantum information in the data qubits from absorption ofphotons emitted from nearby ancilla qubits. As a result, there is nodecoherence from this measurement process and mid-circuit partialreadout of the ion register can be performed without any constraints onthe distance between data and ancilla ion qubits. Furthermore, only asingle species ion is used, so entangling gates between data and ancillaions will typically be of higher fidelity.

Mid-Circuit Remote Entanglement Generation

Ion-based quantum computers will need to scale to numbers of qubits thatare larger than can be worked with in a single trap. A technique called“remote entanglement generation” (REG) may be required to enablecommunication between the registers of ions held in separate traps. Acommon method of remote entanglement generation involves combiningsingle photons emitted by “ancilla” ions in separate traps onto abeamsplitter and measuring the output of that beamsplitter. During theprocess of REG, ancilla ions are typically kept in the g-type space andemit many photons, only a small fraction of which can be typicallycollected and used in the beamsplitter interference protocol mentionedabove. The remainder of these photons are scattered in all directionsand can be reabsorbed by neighboring quantum data ions that are also inthe g-type space. If these neighboring data ions have quantuminformation in them (as would be the case for REG attempted in themiddle of a quantum algorithm as might often be desirable), thisinformation will be lost. If all ions are in the g-type space (which isthe standard approach), REG cannot be carried out without sufferingdecoherence or without keeping the ancilla ions very far away from thedata ions (the latter of which is not practical or desirable in manysituations). The use of dual-species trapped-ion systems, where ancillasand data ions are different species, also mitigates this problem andallows ions to stay close to one another. However, the disadvantages ofdual-species operation have already been elucidated earlier. Inmid-circuit REG using dual-species, entangling (two-qubit) gates wouldbe required to distribute the quantum information around the quantumregister, and such dual-species gates typically have worse fidelity thansingle-species entangling gates.

There are various advantages to the approach described herein inconnection with mid-circuit remote entanglement generation. For example,it is possible to protect the neighboring ions in the m-type spaceduring REG, as the m-type ions cannot absorb photons emitted from g-typeions. As a result, REG can be performed in the middle of a quantumcircuit using REG ancilla ions without causing decoherence of nearbyquantum data ions. Furthermore, in our approach, only a single speciesion is used, so entangling gates between data and ancilla ions willtypically be higher fidelity.

Advantages of Dual Spaces Over Dual Species

The advantages of dual spaces over dual species are described, at leastpartially, in connection with FIG. 1 . For example, using the dual-spaceapproach, m-type qubits are protected from stray control or scatteredlight in entropic operations (e.g., sympathetic Doppler, EIT cooling,REG) in neighbors. The dual-space approach enables mid-circuit cooling,calibration, readout, REG. The use of one species means fewer lasers andoptical paths, standard, efficient sympathetic cooling, morestraightforward shuttling, chain reordering accomplished via HSS(dynamic reconfigurability of the chain with lasers), and REdistribution accomplished via HSS and not a mixed-species two-qubit (2q)gate.

Two Classes of Features: CLASS I—Qubits Plus Coolant/Calibration Ions

The first class of features, CLASS I, is described in connection withFIG. 2 . In connection with CLASS I the following scheme can beperformed (as illustrated in FIG. 2 ):

(1) Initialize: Separate qubits and coolant ions into g (e.g., S_(1/2)in ¹³³Ba⁺ and m (e.g., D_(5/2)) manifolds. Transfer only coolant ions tom manifold.

(2) Perform part of algorithm on g-type qubits.

(3) Mid-algorithm, flip-flop (HSS) all ions between g and m manifolds,with qubits and coolant ions in opposite manifolds at all times. Theg-type has Raman, laser cooling, low-fidelity readout, pumping. Them-type has storage. Repeat 2-3 until the algorithm completes.

(4) Transfer qubits to o-type for high-fidelity readout.

The use of CLASS I enables: (1) Sympathetic cooling of any flavor withperfect mass-matching, coolant ion placement reconfigurable on aper-circuit basis without physical shuttling, and (2) mid-circuitcalibration routines on coolant ions that have hyperfine qubit statesidentical to those of the qubits.

Two Classes of Features: CLASS II—Qubits Plus Ancillas Plus Coolant Ions

The second class of features, CLASS II, is described in connection withFIG. 3 . In connection with CLASS II the following scheme can beperformed (as illustrated in FIG. 3 ):

(1) Perform partial algorithm with data qubits and ancillas in g-type.

(2) Transfer only ancillas to o-type and data to m-type via HSS andhi-fidelity readout of ancillas.

(3) Move ancilla qubits back to qubit manifold and continue circuit.

(4) Sympathetic cooling/calibration can also be interspersed at any time(See Classes I and II).

CLASS II functions require more HSS than CLASS I, but both need ONLYlocal g-type Raman and global HSS, cooling, and readout.

The use of CLASS II enables: (1) Mid-circuit partial high-fi readout ofquantum register without physical shuttling, and (2) mid-circuit REGwithout physical shuttling (not depicted).

EXAMPLE (A) Sympathetic Cooling/Calibration

An example of sympathetic cooling/calibration is described in connectionwith FIG. 4 . In connection with FIG. 4 the following scheme can beperformed (which follows the diagrammatic flow in FIG. 4 from top tobottom):

(1) Initialize all to |0>_(g) via optical pumping (OP).

(2) Local g-type Raman of data to |1>_(g).

(3) Global HSS of |0>_(g)⇄|0>_(m).

(4) Algorithm via g-type 1 and 2-qubit Raman gates.

(5A) Global HSS of |0>_(g)⇄|0>_(m); |1>_(g)⇄|1>_(m) (m-type).

(6Ai) Global sympathetic cooling in g-type space.

(6Aii) Calibration via local Raman and “low-fi” or low-fidelity readouton coolant: Ramsey, carrier Rabi (B-field, etc.), sideband Rabi (trapfrequency).

(7A) Global HSS of |0>_(g)⇄|0>_(m); |1>_(g)⇄|1>_(m).

Repeat 4-7.

EXAMPLE (A-Alternative) Sympathetic Cooling/Calibration

An example of an alternative sympathetic cooling/calibration requiringHSS beam with only m-type splitting is described in connection with FIG.5 . In connection with FIG. 5 the following scheme can be performed(which follows the diagrammatic flow in FIG. 5 from top to bottom):

(1) Initialize all to |0>_(g) via OP.

(2) Local g-type Raman of data to |1>_(g).

(3) Global HSS of |0>_(g)⇄|0>_(m).

(4) Algorithm via g-type 1 and 2-qubit Raman gates.

(5A) Global HSS of |0>_(g)⇄|0>_(m) (o-type).

(6A) Local OR global g-type Raman of all ions; since global is OK, thiscould be u-wave driven.

(7A) Global HSS of |0>_(g)⇄|1>_(m) (m-type).

(8Ai/ii) Global sympathetic cooling in g-type space/cal.

(9A) Reverse steps 7A-5A.

EXAMPLE (B) Ancilla Readout

An example of an ancilla readout is described in connection with FIG. 6. In connection with FIG. 6 the following scheme can be performed (whichfollows the diagrammatic flow in FIG. 6 from top to bottom):

(1) Initialize all to |0>_(g) via OP.

(2) Local g-type Raman of data to |1>_(g).

(3) Global HSS of |0>_(g)⇄|0>_(m).

(4) Algorithm via g-type 1 and 2-qubit Raman gates.

(5B) Global HSS of |1>_(g)⇄|1>_(m) (both qubits o-type).

(6B) Local g-type Raman of ancilla to |1>_(g).

(7B) Global HSS of |0>_(g)⇄|0>_(m) (o-type ancilla, m-type data).

(8B) Readout only ancilla with global detection lasers and pump to|0>_(g).

(9B1) Global HSS of |1>_(m)⇄|1>_(g).

(9B2) Local g-type Raman on ancilla conditioned on ancilla readout.

(10B) Global HSS of |0>_(m)⇄|0>_(g)→5A.

EXAMPLE (C) Mid-Algorithm Calibration Via Ancilla

An example of a mid-algorithm calibration via ancilla is described inconnection with FIG. 7 . In connection with FIG. 7 the following schemecan be performed (which follows the diagrammatic flow in FIG. 7 from topto bottom):

(1) Initialize all to |0>_(g) via OP.

(2) Local g-type Raman of data to |1>_(g).

(3) Global HSS of |0>_(g)⇄|0>_(m).

(4C) Calibration via local Raman on ancilla: Ramsey, carrier Rabi(B-field, etc.), sideband Rabi (trap frequency).

(5B) Global HSS of |1>_(g)⇄|1>_(m).

(6B) Local g-type Raman of ancilla |1>_(g).

(7B) Global HSS of |0>_(g)⇄|0>_(m) (creates o-type ancilla).

(8B) Readout only ancilla with global detection lasers.

(9B1) Global HSS of |1>_(m)⇄|1>_(g).

(9B2) Local g-type Raman on ancilla conditioned on ancilla readout.

(10B) Global HSS of |0>_(m)⇄|0>_(g)→5A.

EXAMPLE (D) Reg and Distribution Via Ancilla

An example of a REG and distribution via ancilla is described inconnection with FIGS. 8 and 9 . In connection with FIG. 8 the followingscheme can be performed (which follows the diagrammatic flow in FIG. 8from top to bottom):

(1) Initialize all to |0>_(g) via OP.

(2) Local g-type Raman of data to |1>_(g).

(3) Global HSS of |0>_(g)⇄|0>_(m).

(4C) Calibration via local Raman on ancilla: Ramsey, carrier Rabi(B-field, etc.), sideband Rabi (trap frequency).

(5B) Global HSS of |1>_(g)⇄|1>_(m).

(6B) Local g-type Raman of ancilla |1>_(g).

(7B) Global HSS of |0>_(g)⇄|0>_(m) (creates o-type ancilla).

(8B) Readout only ancilla with global detection laser.

(9D) REG attempts and sympathetic cooling interleaved.

In connection with FIG. 9 the scheme described above is continued (byfollowing the diagrammatic flow in FIG. 9 from top to bottom):

Step (9D) is now shown at the top and was last step shown in FIG. 9 .(9D) REG attempts and sympathetic cooling interleaved.

(10D) Global HSS of |0>_(g)⇄|0>_(m)

(11D) Local g-type Raman on REG ancilla.

(12Di) Global HSS of |1>_(g)⇄|1>_(m)

(12Dii) Global HSS of |0>_(g)⇄|0>_(m)

(13D) Local g-type Raman on REG ancilla.

(14D) Global HSS of |0>_(g)⇄|0>_(m)

(15D) Entanglement distribution in g-type using single species 2q gates.

Hilbert Space Shuttling (HSS)

In connection with HSS, questions may come up about how good the 1762-nmpulses are. Blatt/Home claim fidelities of 5e⁻⁵ in ⁴⁰Ca⁺ (729 nm) andothers have been able to do ˜4e⁻⁴ in ⁸⁸Sr⁺ (674 nm, GST). One aspectincludes potentially using composite pulses to improve. Moreover, the1762 pulse is likely to be better than 674, 729 pulses due to smallerDebye-Waller factors (DWs). But probably may want to use the global 1762along radial direction to keep DWs low.

Another possible consideration relates to the 1762 pulse phase. Theoptical phase gets imprinted on the o-type but gets removed whenconverting back to g-type as long as laser is coherent over o-type dwelltime. For the o-type, coherence times of 10-100 milliseconds (ms) areachievable.

For the m-type, only the phase difference between the |0>_(g)⇄|0>_(m)and |1>_(g)⇄|1>_(m) beams matters. One approach is to derive both beamsfrom same laser, minimize path length differences.

Another question that may come up is the AC Stark shifts from global1762 pulses. For the g-type: Δ=10 GHz gives δ_(AC)˜25 Hz. For the m-typeΔ=80 MHz gives δ_(AC)˜3 kHz. Only occurs for F=1 to F′=3 beam (F=0 toF′=3 is quadrupole forbidden). Can potentially use spin echo to cancel,or just keep track of the Zgate rotation

Yet another question that may come up is the number of 1762 tones/lasersthat may be needed. The scheme described above needs independent 1762tones separated by ˜10 GHz. An example of such implementation isdescribed below. A modified version only requires 1762 tones separatedby ˜80 MHz mid-circuit REG is given up. However, REG is a longer-termgoal with other technical challenges to consider.

M-Type Raman Gates

Other aspects of the present disclosure may include implementing m-typeRaman gates. M-type Raman gates may implement the same classes offeatures as in the g-type Raman scheme as described below. An example ofm-type Raman gates is described in connection with FIG. 10 .Fundamentally higher-fidelity gates for ¹³³Ba⁺ with Raman laser at 532nm. D_(5/2) only couples to P_(3/2) so it is possible to get 1/Δ Rabirate even for Δ>>ω_(HFS). Wins the war against spontaneous emission(˜1/Δ²)→˜—5× error reduction.

This approach is technically simpler, with straightforward CW Raman ifdesired. CW Raman also can be used for g-type Raman. Can use AOM insteadof EOM to span qubit frequency.

In addition, circuit performance is largely insensitive to imperfectHSS. The need for HSS transfers during the computation is either reduced(Class II functions) or eliminated altogether (Class I functions), whichsignificantly reduces the impact of imperfect HSS transfer on thecomputation fidelity.

Two Classes of Features with M-Type Raman: CLASS I—Qubits PlusCoolant/Calibration Ions

The first class of features with m-type Raman, CLASS I, is described inconnection with FIG. 11 shown below. In connection with CLASS I thefollowing scheme can be performed (as illustrated in FIG. 11 ):

(1) Initialize: Separate qubits and coolant ions into g (S_(1/2)) and m(D_(5/2)) manifolds with global HSS. Transfer only qubit ions to mmanifold.

(2) Run circuit in m manifold (now has Raman) while interspersingcooling/calibration with ions in g manifold (has Raman, EIT cooling,readout, pumping). No HSS required during circuit/cooling/calibration.

(3) Transfer one qubit state to o-type for high-fidelity readout ofqubits with global HSS.

The use of CLASS I enables (without HSS duringcircuit/cooling/calibration): (1) Sympathetic cooling of any flavor withperfect mass-matching, coolant ion placement reconfigurable on aper-circuit basis without physical shuttling, and (2) Mid-circuitcalibration routines on coolant ions that have hyperfine qubit statesidentical to those of the qubits. The use of CLASS I requires only|0>_(g)⇄|0>_(m) transitions for HSS, no m-type AC Stark shifts. Also, itrequires only m-type Raman, not g-type.

Two Classes of Features with M-Type Raman: CLASS II—Qubits Plus AncillaePlus Coolant Ions

The second class of features with m-type Raman, CLASS II, is describedin connection with FIG. 12 . In connection with CLASS II the followingscheme can be performed (as illustrated in FIG. 12 ):

(1) Perform partial algorithm with data qubits and ancillas in m-type.

(2) Transfer only ancillas to o-type and data to m-type via HSS andhi-fi readout of ancillas.

(3) Move ancilla qubits back to qubit manifold and continue circuit.

(4) Sympathetic cooling/calibration can also be interspersed at any time(Class A is a subset of B).

As before, Class II functions require more HSS than Class I, but bothneed ONLY local m- and g-type Raman and global HSS, cooling, andreadout.

The use of CLASS II enables: (1) Mid-circuit partial readout of quantumregister without physical shuttling, and (2) mid-circuit REG withoutphysical shuttling.

Scheme for Nulling HSS Laser Phase Noise by Driving Both HSS TransitionsSimultaneously (CLASS I Functions)

One source of error in this approach can be phase noise in the laserused to drive the HSS transition. This noise is technical but intrinsic;it can be reduced by locking the laser phase to a suitably stablereference, but it cannot be completely eliminated. In particular, thislaser phase noise might impart phase noise onto our qubits every time aswap of the ancilla and qubit ions between the g and m manifolds takesplace. For example, by driving the |0>_(g) to |0>_(m) HSS transitionfollowed sequentially by the |1>_(g) to |1>_(m) transition (or viceversa), then any drift in the laser phase between the times of these twotransitions is imprinted into a relative phase between |0>_(m) and|1>_(m), which enters into and degrades the fidelity of the calculation.

In other words, in performing the two HSS transitions sequentially,there is a brief storage of the qubit information in the optical qubit,when the qubit is divided between the g and m manifolds. During thistime, any drift between the phases of the optical qubit and laser isimprinted on the qubit phase when the transfer is completed to the mmanifold.

The techniques described herein can be used as a solution to the problemoutlined above. The impact of laser phase noise on the qubit phase canbe nulled by driving the |0>_(g) to |0>_(m) and |1>_(g) to |1>_(m)transitions simultaneously. The laser phase at the transition is commonto both |0>_(m) and |1>_(m) and therefore does not introduce anerroneous phase into the calculation. In other words, the qubitinformation is at no time stored in the optical qubit, eliminating theopportunity for laser phase noise to be converted into qubit phaseerror.

If the laser phase noise is sufficiently large, it can cause imperfecttransfer (i.e., the population in |0>_(g) is not fully transferred to|0>_(m)), but, as elucidated elsewhere, this scheme is sufficientlygeneral so as to enable to use BB1 or other pulse sequences, which aredesigned to optimize transfer even in the presence of experimentalimperfections like phase noise. Further, an error of imperfect transfer,unlike an error of laser phase being imprinted onto the qubit, can beeasily detected, in which case it is possible to choose to either rejectthe calculation result if it is impacted by the error or accept thecalculation result if it is not.

This solution is particularly useful for the Class I functions in thescheme that does not use m-state Raman, wherein it always drives the twoHSS transitions together in the midst of the calculation (i.e., notduring initialization and readout). Therefore, this technique caneliminate the impact of laser phase noise on the qubit phase foralgorithms that use only Class I functions.

Scheme for Nulling HSS Laser Phase Noise by Performing an Echo Sequence(CLASS II Functions)

The technique of driving the |0>_(g) to |0>_(m) and |1>_(g) to |1>_(m)transitions simultaneously to prevent laser phase noise from beingimprinted on the qubit only works when no other operations need to beperformed in between these two transitions. This is not the case forClass II transitions. For example, for ancilla readout, one HSStransition (either |0>_(g) to |0>_(m) or |1>_(g) to |1>_(m)) is driven,then select out the ancilla ions to read out by applying a Raman pulseto those ions, and then drive the other HSS transition. Because theRaman transition inevitably has a finite duration, this sequence issusceptible to imprinting laser phase noise onto the qubit phase noise.

In other words, storing the qubit information in an optical qubit for afinite amount of time will be needed, creating the opportunity for laserphase noise to be converted into qubit phase error.

The techniques described herein can be used as a solution to the problemoutlined above. For example, a technique called “spin echoing,” which iscommon in the NMR and quantum information communities, can be adaptedfor use with the scheme/architecture described herein. The basic conceptis that the phase noise in the laser is transferred to the qubit whenthe qubit information is imprinted on the optical qubit during the Ramanpulse. To “echo out” this phase error, an echo pulse is applied to theoptical qubit after the Raman pulse by driving the |0>_(g) to |0>_(m)and |1>_(g) to |1>_(m) transitions simultaneously, which has the effectof flipping the optical qubit. This causes the laser phase noise to beimprinted on the optical qubit with the opposite sign. There is a waitafter the echo pulse for a period of time equal to the duration of theRaman pulse before completing the transition to the m manifold, so theerrors imprinted before and after the echo pulse cancel each other. Ifthe rate at which the laser phase drifts is constant, then thiscancellation can, in principle, be perfect. This echo techniquetherefore eliminates the OMG scheme's susceptibility to a laser phasethat drifts at a constant rate, rendering the scheme instead susceptibleonly to the change in the rate at which the laser phase drifts over thecourse of the echo sequence.

An additional level of echoing can be applied to further reduce theOMG's scheme's susceptibility to laser phase noise over the course ofperforming a Class II function. In the case of mid-circuit ancillareadout, it is possible to echo the phase noise as described above whileseparating out the readout ancillae from the other qubits. Also need toreverse this operation after performing the readout in order to fold thereadout ancillae back into the qubit register. By applying additionalecho pulses to this second operation, it is possible to null thescheme's susceptibility not only to a laser phase that drifts at aconstant rate but also to a laser phase that drifts at a rate that isitself changing at a constant rate over the course of the entire readoutoperation. Essentially, the sequence of HSS transitions is driven insuch a way that if, for example, the optical qubit acquired phase noisewith a positive sign followed by a negative sign for the initialancillae-separation sequence, it acquires phase error with a negativesign followed by a positive sign for the ancillae-refolding sequence.Therefore, not only are the ancillae-separation and ancillae-refoldingsequences themselves individually echoed to cancel phase error acquiredwithin each sequence, but they are constructed in such a way that thephase noise acquired during the ancillae-refolding sequence cancels thatacquired during the ancillae-separation sequence.

Schemes for High-Fidelity HSS with a Global Beam

A problem that may arise is that for a laser beam of finite sizeglobally addressing a long chain of ions from a direction that is notalong the chain axis, there will be a limit to the fidelity of thepi-pulses due to inhomogeneity of the laser intensity over the chain.For example, a 32-ion chain with 3-micron ion spacing; global beam with85-micron radius centered on chain, propagating normal to the chain axisgives pi-pulse fidelity of only 0.84 for the edge ions (1 and 32) if thelaser intensity is chosen to drive a perfect pi-pulse on the center ion.

This disclosure provides two exemplary embodiments (e.g., exemplaryschemes or aspects) that address the problem outlined above.

Scheme 1: Make the laser beam larger only in the direction along thechain axis (high-eccentricity elliptical beam). In the example above,make the beam radius 600 microns to get HSS error on outer ions to<1e-4. This will require 2.66× the time for the pi-pulse HSS transferfor the same laser power.

Scheme 2: Use a coherent quantum pulse sequence to minimize pi-pulseinfidelity due to inhomogeneous laser intensity. One can use the BB1sequence (e.g., http://cds.cern.ch/record/599468/files/0301019.pdf for ageneral outline of BB1) and the same (e.g., 85 micron) beam size(low-eccentricity elliptical beam). This can also achieve <1e-4 HSSerrors but would take 1.9× longer than scheme.

Scheme 1 vs Scheme 2: Scheme 2 is better if it is undesirable to have alarge beam for optical access reasons. Scheme 1 is better if one wantsfaster HSS transfer (for fixed laser power) or smaller required laserpower (for fixed transfer time). Another advantage of Scheme 1 is thatby not requiring BB1, pulse sequences can be used that are optimized forother kinds of transfer errors (e.g., frequency or phase noise).

Laser Scheme for High-Fidelity Dual-Space Operation

A laser scheme for high-fidelity dual-space operation is described inconnection with FIG. 13 . This laser beam scheme (propagationdirection/polarizations/B-field orientation) is very well suited tohigh-fidelity dual-space operation.

Individual Raman configuration minimizes deleterious AC Stark shiftswhen using pulsed lasers.

Global HSS is typically driven by an atomic quadrupole transition. TheHSS beam orientations shown in FIG. 13 maximize the transition rate. Forlong-wavelength HSS laser (e.g., 1762 nanometer (nm) for Ba+ ions), thesmall Lamb-Dicke parameter results in small HSS transfer errors (<1e-4)even for significant thermal population of axial modes (nbar=50) in a32-ion chain.

The polarization of the HSS beam depends on the specific sattes in them-state manifold that are used during the HSS sequence. For clock states(i.e., those with m_(F)=0), a polarization perpendicular to the magneticfield may be utilized to maximize the transition rate. However, thereare other states (so-called “first-order field-insensitive” or “FOFI”states) that have nonzero values of m_(F) but whose relative frequenciesare insensitive to magnetic fields to first order. For these states,which have |m_(F)|=1, the transition rate is maximized by setting thepolarization to lie in the plane defined by the direction of beampropagation and the magnetic field.

Scheme to Enable Simultaneous Driving of One or Two HSS TransitionsUsing an AOM and EOM

There is a need to implement a technical solution that enables drivingeither (1) the |0>_(g) to |0>_(m) and |1>_(g) to |1>_(m) transitionssimultaneously or (2) transition individually. Because these transitionscan be separated in frequency by many GHz for many ion species, this maybe technically challenging.

In an exemplary aspect, this is accomplished by using an electro-opticmodulator (EOM) to apply two sets of sidebands so that one sideband fromeach set addressed each transition. These two sets of sidebands couldthen be turned on together or individually to drive one or bothtransitions. However, this would unavoidably divide the optical powerbetween five tones (two in each set of sidebands plus the carrier),which would raise the power that is required from the optical systemupstream of the EOM.

Alternatively, this is accomplished in an exemplary aspect by using anacousto-optic modulator (AOM) and EOM in series. The EOM would modulatethe laser frequency to address the two transitions, one with the EOMcarrier and one with one sideband. This reduces the amount of power thatwould be wasted since only one set of sidebands would need to begenerated. However, since the power in the carrier cannot be nulled, theAOM is needed to modulate the overall power in the beam. For thisapproach, it would be easy to address both transitions and to addressonly the transition addressed by the EOM carrier by turning off the EOMsideband, but it would be difficult to address only the transitionaddressed by the EOM sideband. To accomplish this, the drive frequenciesof both the EOM and AOM could be shifted by equal amounts to detune thecarrier away from its transition but leave the carrier resonant with itstransition. However, in this case, the finite bandwidth of the AOM,which is often limited to a few tens of MHz unless special measures aretaken, would force us to balance off-resonant excitation of the unwantedtransition versus the speed at which the transition is driven.

A solution to the problem outlined above is to use an AOM and EOM insequence, as in the second scheme listed above, but with the extensionof using independent control of the AOM and EOM phases to cancelexcitation of the unwanted transition. The phase of the optical tonecorresponding to the EOM carrier is given by the phase of the AOM drivephase alone, but the phase of the optical tone corresponding to the EOMsideband is given by the sum of the phases of the AOM and EOM drivetones. As described elsewhere, the BB1 and related composite pulsesequences consist of a nominal rotation pulse followed by somecorrection pulses whose rotation angles are fixed but whose phasesdepend on the nominal rotation angle. Halfway through the nominalrotation pulse, it is possible to change the phases of the AOM and EOMdrive tones by pi. This results in the phase of the carrier optical tonechanging by pi and the phase of the sideband optical tone changing by2*pi, which is equivalent to its phase remaining unchanged. Thus, thesideband transition gets a nominal rotation angle of pi, and the carriertransition gets a nominal rotation angle of 0. Then the correctionpulses are applied on both transitions, using the same technique withthe AOM and EOM phases to give the correction pulses the proper phasesfor nominal angles of 0 and pi.

This scheme can be extended to the case where the strengths of the twoHSS transitions are equal (i.e., the two transitions are driven at equalrates for a given optical power). In this case, the two transitions canbe driven with the same set of EOM sidebands, which are intrinsicallypower-matched. This obviates the need to precisely calibrate the powerof the optical powers of the EOM sidebands to match that of the EOMcarrier. In this case, the phase of one optical tone is given by the sumof the phases of the AOM and EOM drives, and the phase of the otheroptical tone is given by their difference. Halfway through the nominalrotation pulse, it is possible to change the phase of the AOM drive by+pi/2 and the phase of the EOM drive by either +pi/2 or −pi/2. Thisresults in the phase of one of the optical tones changing by pi and thephase of the other remaining unchanged. As above, one of the transitionsgets a nominal rotation angle of pi, and the other gets a nominalrotation angle of 0. Then the correction pulses are applied on bothtransitions, again setting the phases of the AOM and EOM drive to givethe correction pulses the proper phases for nominal angles of 0 and pi.This technique enables to drive either transition, and it is possible todrive both by not changing the phases of the AOM and EOM drives.

In general, the dual-space, single-species architecture for trapped-ionfor quantum information processing described herein is flexible and hasseveral advantages over architectures that rely on dual species. Forexample, a single chain of ions is reconfigurable as needed withoutphysical shuttling. Also, sympathetic cooling can be perfectlymass-matched. It should be appreciated that the exemplary aspects hereindo not require narrow line cooling, which itself may be a risk, and maynot get as cold as (electromagnetically-induced-transparency) EITcooling. This approach also enables mid-algorithm readout and remoteentanglement generation (REG) on dipole-allowed (broad) transitions forhigh speed. Moreover, no mixed-species two-qubit (2q) gate for REdistribution.

The use of a global 1762 optical beam for dual-space, single-speciesarchitectures is already considered for shelving during readout. Onlythe short-wavelength Raman need be focused tightly for addressing. Butfor the approach using g-type gates (ground qubit gates), anotherindependent tone may be needed 10 GHz away. This may be accomplishedwith a second laser and a high frequency acousto-optic modulator (AOM).AC Stark shifts of the m-type (metastable qubit), including from the iontrap RF, needs to be considered/managed. The global 1762 optical beamwould also allow for integrated photonics down the road.

The dual-space, single-species architecture can also support m-typeRaman operations, which can produce higher-fidelity and more efficientgates. Such an approach only needs the 1762 tones spaced by ˜80 MHz (not10 GHz) with local m-type and g-type Raman.

FIG. 14 is a block diagram that illustrates an example of a QIP system1400 in accordance with aspects of this disclosure in which thetechniques described above for a dual-space, single species trapped-ionarchitecture can be implemented. The QIP system 1400 may also bereferred to as a quantum computing system, a computer device, a trappedion system, or the like.

The QIP system 1400 can include a source 1460 that provides atomicspecies (e.g., a plume or flux of neutral atoms) to a chamber 1450having an ion trap 1470 that traps the atomic species once ionized(e.g., photoionized). The ion trap 1470 may be part of a processor orprocessing portion of the QIP system 1400. The source 1460 may beimplemented separate from the chamber 1450.

The imaging system 1430 can include a high-resolution imager (e.g., CCDcamera) for monitoring the atomic ions while they are being provided tothe ion trap or after they have been provided to the ion trap 1470. Inan aspect, the imaging system 1430 can be implemented separate from theoptical and trap controller 1420, however, the use of fluorescence todetect, identify, and label atomic ions using image processingalgorithms may need to be coordinated with the optical and trapcontroller 1420.

The QIP system 1400 may also include an algorithms component 1410 thatmay operate with other parts of the QIP system 1400 (not shown) toperform quantum algorithms or quantum operations, including a stack orsequence of combinations of single qubit operations and/or multi-qubitoperations (e.g., two-qubit operations) as well as extended quantumcomputations. As such, the algorithms component 1410 may provideinstructions to various components of the QIP system 1400 (e.g., to theoptical and trap controller 1420) to enable the implementation of thequantum algorithms or quantum operations.

Referring now to FIG. 15 , illustrated is an example computer system ordevice 1500 in accordance with aspects of the disclosure. The computerdevice 1500 can represent a single computing device, multiple computingdevices, or a distributed computing system, for example. The computerdevice 1500 may be configured as a quantum computer (e.g., a QIPsystem), a classical computer, or a combination of quantum and classicalcomputing functions. For example, the computer device 1500 may be usedto process information using quantum algorithms based on trapped iontechnology and may therefore implement the dual-space, single speciesarchitecture described herein. A generic example of the computer device1500 as a QIP system is illustrated in the QIP system 1400 shown in FIG.14 .

In one example, the computer device 1500 may include a processor 1510for carrying out processing functions associated with one or more of thefeatures described herein. The processor 1510 may include a single ormultiple set of processors or multi-core processors. Moreover, theprocessor 1510 may be implemented as an integrated processing systemand/or a distributed processing system. The processor 1510 may include acentral processing unit (CPU), a quantum processing unit (QPU), agraphics processing unit (GPU), or combination of those types ofprocessors. In one aspect, the processor 1510 may refer to a generalprocessor of the computer device 1500, which may also include additionalprocessors 1510 to perform more specific functions such as functions forindividual beam control.

In an example, the computer device 1500 may include a memory 1520 forstoring instructions executable by the processor 1510 for carrying outthe functions described herein. In an implementation, for example, thememory 1520 may correspond to a computer-readable storage medium thatstores code or instructions to perform one or more of the functions oroperations described herein. Just like the processor 1510, the memory1520 may refer to a general memory of the computer device 1500, whichmay also include additional memories 1520 to store instructions and/ordata for more specific functions such as instructions and/or data forindividual beam control.

Further, the computer device 1500 may include a communications component1530 that provides for establishing and maintaining communications withone or more parties utilizing hardware, software, and services asdescribed herein. The communications component 1530 may carrycommunications between components on the computer device 1500, as wellas between the computer device 1500 and external devices, such asdevices located across a communications network and/or devices seriallyor locally connected to computer device 1500. For example, thecommunications component 1530 may include one or more buses, and mayfurther include transmit chain components and receive chain componentsassociated with a transmitter and receiver, respectively, operable forinterfacing with external devices.

Additionally, the computer device 1500 may include a data store 1540,which can be any suitable combination of hardware and/or software, whichprovides for mass storage of information, databases, and programsemployed in connection with implementations described herein. Forexample, the data store 1540 may be a data repository for operatingsystem 1560 (e.g., classical OS, or quantum OS). In one implementation,the data store 1540 may include the memory 1520.

The computer device 1500 may also include a user interface component1550 operable to receive inputs from a user of the computer device 1500and further operable to generate outputs for presentation to the user orto provide to a different system (directly or indirectly). The userinterface component 1550 may include one or more input devices,including but not limited to a keyboard, a number pad, a mouse, atouch-sensitive display, a digitizer, a navigation key, a function key,a microphone, a voice recognition component, any other mechanism capableof receiving an input from a user, or any combination thereof. Further,the user interface component 1550 may include one or more outputdevices, including but not limited to a display, a speaker, a hapticfeedback mechanism, a printer, any other mechanism capable of presentingan output to a user, or any combination thereof.

In an implementation, the user interface component 1550 may transmitand/or receive messages corresponding to the operation of the operatingsystem 1560. In addition, the processor 1510 may execute the operatingsystem 1560 and/or applications or programs, and the memory 1520 or thedata store 1540 may store them.

When the computer device 1500 is implemented as part of a cloud-basedinfrastructure solution, the user interface component 1550 may be usedto allow a user of the cloud-based infrastructure solution to remotelyinteract with the computer device 1500.

In some aspect, the conventional dual-space single-species architecture,where all Raman operations may be performed in the S states, is expectedto work well for single-chain operation. However, there may be apotential roadblock to scaling this technique to multi-chain operationwith repeated cooling cycles. Aspects of the present disclosure includesa mitigation strategy using D-state Raman in Ba-137. Specifically, forthe current approach (where Raman is performed in the S states), errorsmay accrue each time the qubits are shelved or deshelved. Assuming thatthe clock laser does not impart a phase error onto the qubits (whichshould be the case if simultaneous clock transitions are driven), theremay be errors in the transfer from S to D. Importantly, these may besubspace leakage errors, which may be particularly difficult to correctwith traditional quantum error-correction codes. If there is a per-ionclock transfer fidelity of 99.5%, that gives a success rate of 20% whenexecuting an algorithm with 23 qubits and 3 cycles of sympatheticcooling plus initialization [0.995{circumflex over( )}((2*3+1)*23)=0.2]. This error may be detected fairly easily byreading out only the coolant ions at the end of the run, and throwingout bad runs and convert an algorithmic fidelity loss into a yield loss,but may start to become prohibitive quickly when scaling up to many tensof qubits.

The alternate form of dual-space single-species architecturalimplementation with D-state Raman may reduce the impact ofclock-transition errors because the qubits do not need to be shelved anddeshelved in order to perform sympathetic cooling or mid-circuitcalibration with the coolant ions. However, the partial readout maystill be needed to perform error correction. In another scheme, allqubits still need to be shelved and deshelved at least twice in order toperform partial readout, and the scheme may echo out the impact of thephase noise of the clock laser, which may require even moreshelve-deshelve round trips. This will impose a minimum impact of theclock transfer error for each error correction cycle, which scaleslinearly with the number of qubits. This scheme may be an improvementover the S-state Raman scheme, but further improvements may bedesirable.

Therefore, it may be desirable to further minimize the number of S-Dround trips taken by the qubits, which is where the trap-door operationis implemented.

FIG. 16 illustrates an example of Ba-137 level structure with allowedtransitions between clock states according aspects of the presentdisclosure. Aspects of the present disclosure may relate to operationsduring computations of quantum circuits above. For example, thetransitions shown in FIG. 16 may be used for the trap-door mid-circuitreadout scheme and/or the trap-door loading scheme described below.

Aspects of the present disclosure may including performing Raman in theD states and working with clock states. For Ba-133, there may be twoclock states in both the S and D manifolds. At least some of the statesmay be used as qubit states. In Ba-137, there may be a larger set ofstates and transitions as shown in FIG. 16 . These concepts also applyif a set of states in the D manifold other than the clock states (e.g.,first-order field-insensitive or FOFI states) are selected to be used asqubits.

In some aspects, 1′ and 2′ may be selected as the D-state qubit statesbecause 3′ and 4′ are separated by approximately 500 kilohertz (kHz).The 3′ and 4′ states, though not used as qubit states, may be coupled tothe D-state qubit states 1′ and 2′ by Raman transitions, and to theS-state qubit states 1 and 2 by clock transitions. Therefore, the 3′ and4′ states may provide a “trap-door” out of the qubit subspace by whichthe population may be shuttled back and forth between S and D.

FIG. 17 illustrates an example of trap-door mid-circuit readout. In someaspects, the scheme shown in FIG. 17 illustrates a technique for usingthe trap-door to perform a mid-circuit measurement. First, the ancillaions are driven from 1′ to 3′ via Raman transitions. Next, the 1′component of the ancilla ions population state may be transferred from3′ to 1 in the S state. Because the ancilla ions may be separated fromthe qubit ions with individually-addressed Raman first, and then theglobal clock beam second, this sequence may allow for the transfer ofonly the ancilla ions to the S state. The qubit ions may not be drivenin the clock transition, and therefore, they do not experienceclock-related errors. The coolant ions in S may be pumped from the 1manifold to the 2 manifold prior to starting the readout sequence.

According to aspects of the present disclosure, under the trap-doorscheme, the qubits ions are not addressed with the clock laser, avoidthe problem described above.

In some aspects, the qubit ions may be susceptible to clock transfererror when performing partial readout. However, the clock transfer errormay be reduced by driving repeated clock pi pulses from 3′ to 1 withoptical pumping from 1 to 2 in between. Optical pumping in the S statesmay be bi-directional and may depend on the location of the carrier(e.g., 493 carrier). This method may ignore collecting population in theclock S states. Alternatively or additionally to repeated discrete clockand pump pulses, a weak clock drive may be applied and pump beamsimultaneously, continuously pumping population from 3′ to the 2manifold. In some instances, the phase coherence in the ancilla ions maybe negatively impacted. However, the projective measurement may allowthe error-reduction methods described above.

In some instances, the error reduction techniques described herein maybe used to readout the qubit ions at the end of the measurement.Specifically, the clock transition is to be driven from 1′ to 1 directlywithout using the trap door. However, the error-reduction techniques ofapplying either repeated pulses or continuous drives may still beimplemented.

FIG. 18 illustrates an example of trap-door loading according aspects ofthe present disclosure. In some aspects, this technique may beimplemented toward an end of the partial readout sequence to fold theancilla ions back into the qubit array. In other aspects, this techniquemay be utilized at the beginning of the sequence to ensure efficient andverifiable preparation of qubit ions in 1′. In some implementations, at(1), one or more ions may be pumped to 1. Next, at (2), a partial clocktransition drives the one or more ions to 3′. The partial clocktransition may transfer a first portion of the qubit ions populationfrom one state to another. A second portion of the population thatremains in the initial state may constitute an error. At (3), one ormore Raman pulses are used to transfer the qubit ions to 1′. Next, at(4) and (5), the ions in 3′ are flushed back to S using a high fidelitypumping method described above. At (6), both the 1 and 2 manifolds areilluminated to check that only the coolant ions have been pumped to S.If any qubit ion has failed to initialize into 1′, the sequence may berun again, applying the Raman pulses only to the qubit ions that werenot successfully initialized previously. The dynamic method (i.e.,making a second attempt a initializing only those ions that failed onthe first attempt), may be more scalable than other methods of trying toinitialize the entire register until all qubit ions are successfullyinitialized in the same attempt.

Turning to FIG. 19 , a method 1900 of trap-loading may be performed bythe laser scheme of FIG. 13 , the QIP system 1400, subcomponents of theQIP system 1400, the computer device 1500, and/or subcomponents of thecomputer device 1500.

At block 1905, the method 1900 may pump at least one qubit ion from afirst manifold of a first plurality of manifolds to a second manifold ofthe first plurality of manifolds. For example, the QIP system 1400 mayutilize one or more optical beams of the laser scheme to pump at leastone qubit ion from the 2 manifold of the S_(1/2) manifold to the 1manifold of the S_(1/2) manifold.

At block 1910, the method 1900 may drive the at least one qubit ion viaa partial clock transition from the second manifold of the firstplurality of manifolds to a third manifold of a second plurality ofmanifolds. For example, the QIP system 1400 may utilize one or moreoptical beams of the laser scheme to drive the at least one qubit ionvia a partial clock transition from the 1 manifold of the S_(1/2)manifold to the 3′ manifold of the D_(5/2) manifold.

At block 1915, the method 1900 may apply one or more Raman pulses totransfer the at least one qubit ion from the third manifold of thesecond plurality of manifolds to a fourth manifold of the secondplurality of manifolds. For example, the QIP system 1400 may apply oneor more Raman pulses of the laser scheme to transfer the at least onequbit ion from the 3′ manifold to the 1′ manifold of the D_(5/2)manifold.

At block 1920, the method 1900 may flush the at least one qubit ionusing a high-fidelity pumping back to the first plurality of manifolds.For example, the QIP system 1400 may utilize one or more optical beamsof the laser scheme to flush the at least one qubit ion using ahigh-fidelity pumping back to 2 manifold of the S_(1/2) manifold.

At block 1925, the method 1900 may illuminate the first plurality ofmanifolds for verification. For example, the QIP system 1400 may utilizeone or more optical beams of the laser scheme to illuminate the 2manifold to check that only the coolant ions have been pumped to theS_(1/2) manifold.

Aspects of the present disclosure may include a method and/or a systemfor trap-door loading including pumping at least one qubit ion from afirst manifold of a first plurality of manifolds to a second manifold ofthe first plurality of manifolds, drive the at least one qubit ion via apartial clock transition from the second manifold of the first pluralityof manifolds to a third manifold of a second plurality of manifolds,applying one or more Raman pulses to transfer the at least one qubit ionfrom the third manifold of the second plurality of manifolds to a fourthmanifold of the second plurality of manifolds, flushing the at least onequbit ion using a high-fidelity pumping back to the first plurality ofmanifolds, and illuminating the first plurality of manifolds forverification.

Aspects of the present disclosure include the method and/or systemabove, wherein flushing the at least one qubit ion comprises pumping theat least one qubit ion from the third manifold of the second pluralityof manifolds to the second manifold of the first plurality of manifoldsand pumping the at least one qubit ion from the second manifold of thefirst plurality of manifolds to the first manifold of the firstplurality of manifolds.

Aspects of the present disclosure include any of the methods and/orsystems above, wherein the first plurality of manifolds is associatedwith a S_(1/2) manifold and the second plurality of manifolds isassociated with a D_(5/2) manifold.

Aspects of the present disclosure include any of the methods and/orsystems above, further comprising applying one or more additional Ramanpulses to initialize one or more qubit ions of the at least one qubition that failed to initialize during the application of the one or moreRaman pulses.

Aspects of the present disclosure include any of the methods and/orsystems above, further comprising, prior to pumping the at least onequbit from the first manifold or after illuminating the first pluralityof manifolds, applying one or more second Raman pulses to transfer atleast one ancilla ion from the fourth manifold of the second pluralityof manifolds to the third manifold of the second plurality of manifolds,transferring the at least one ancilla ion from the third manifold of thesecond plurality of manifolds to the second manifold of the firstplurality of manifolds, and applying one or more of an individual Ramanbeam or a global beam to separate the at least one ancilla ion from theat least one qubit ion.

Aspects of the present disclosure include any of the methods and/orsystems above, further comprising, prior to applying the one or moresecond Raman pulses, pumping at least one coolant ion from the secondmanifold of the first plurality of manifolds to the first manifold ofthe first plurality of manifolds

Aspects of the present disclosure include any of the method and/orsystem above, wherein applying the global optical beam comprisesapplying a single laser beam having an eccentricity in a direction alongthe plurality of DSSS trapped ions such that the single laser beamcovers the plurality of DSSS trapped ions.

Aspects of the present disclosure include any of the method and/orsystem above, wherein applying the global optical beam comprisesapplying the global optical beam at a first 45-degree angle with respectto the plurality of DSSS trapped ions and a second 45-degree angle withrespect to a magnetic field.

Aspects of the present disclosure include any of the method and/orsystem above, further comprising adjusting a frequency of the at leastone Raman beam of the plurality of Raman beams using an electro-opticmodulator (EOM) or an acousto-optic modulator (AOM) disposed in serieswith an EOM.

Aspects of the present disclosure include any of the method and/orsystem above, further comprising applying a cooling Raman beam of theplurality of Raman beams to at least a cooling ion of the plurality ofDSSS trapped ions to transition the cooling ion from a first state to asecond state that is higher than the first state.

Aspects of the present disclosure include any of the method and/orsystem above, further comprising reading an ancilla ion of the pluralityof DSSS trapped ions associated with the DS SS trapped ion during acomputation of the qubit.

Aspects of the present disclosure include any of the method and/orsystem above, further comprising calibrating the DSSS trapped ion basedon the reading of the ancilla ion during the computation of the qubit.

Aspects of the present disclosure include any of the method and/orsystem above, further comprising performing remote entanglementgeneration between the plurality of DSSS trapped ions and one or moreremote DSSS trapped ions.

The previous description of the disclosure is provided to enable aperson skilled in the art to make or use the disclosure. Variousmodifications to the disclosure will be readily apparent to thoseskilled in the art, and the common principles defined herein may beapplied to other variations without departing from the spirit or scopeof the disclosure. Furthermore, although elements of the describedaspects may be described or claimed in the singular, the plural iscontemplated unless limitation to the singular is explicitly stated.Additionally, all or a portion of any aspect may be utilized with all ora portion of any other aspect, unless stated otherwise. Thus, thedisclosure is not to be limited to the examples and designs describedherein but is to be accorded the widest scope consistent with theprinciples and novel features disclosed herein.

What is claimed is:
 1. A method for trap-door loading in a quantuminformation processing (QIP) system, comprising: pumping at least onequbit ion from a first manifold of a first plurality of manifolds to asecond manifold of the first plurality of manifolds; driving the atleast one qubit ion via a partial clock transition from the secondmanifold of the first plurality of manifolds to a third manifold of asecond plurality of manifolds; applying one or more Raman pulses totransfer the at least one qubit ion from the third manifold of thesecond plurality of manifolds to a fourth manifold of the secondplurality of manifolds; flushing the at least one qubit ion using ahigh-fidelity pumping back to the first plurality of manifolds; andilluminating the first plurality of manifolds for verification.
 2. Themethod of claim 1, wherein flushing the at least one qubit ioncomprises: pumping the at least one qubit ion from the third manifold ofthe second plurality of manifolds to the second manifold of the firstplurality of manifolds; and pumping the at least one qubit ion from thesecond manifold of the first plurality of manifolds to the firstmanifold of the first plurality of manifolds.
 3. The method of claim 2,further comprising repeating the flushing the at least one qubit ion atleast one time.
 4. The method of claim 1, wherein: the first pluralityof manifolds is associated with a S_(1/2) manifold; and the secondplurality of manifolds is associated with a D_(5/2) manifold.
 5. Themethod of claim 1, further comprising applying one or more additionalRaman pulses to initialize one or more qubit ions of the at least onequbit ion that failed to initialize during the application of the one ormore Raman pulses.
 6. The method of claim 1, further comprising, priorto pumping the at least one qubit from the first manifold or afterilluminating the first plurality of manifolds: applying one or moresecond Raman pulses to transfer at least one ancilla ion from the fourthmanifold of the second plurality of manifolds to the third manifold ofthe second plurality of manifolds; transferring the at least one ancillaion from the third manifold of the second plurality of manifolds to thesecond manifold of the first plurality of manifolds; and applying one ormore of an individual Raman beam or a global beam to separate the atleast one ancilla ion from the at least one qubit ion.
 7. The method ofclaim 6, further comprising, prior to applying the one or more secondRaman pulses, pumping at least one coolant ion from the second manifoldof the first plurality of manifolds to the first manifold of the firstplurality of manifolds.
 8. A non-transitory computer readable mediumhaving instructions stored therein that, when executed by one or moreprocessors of a quantum information processing (QIP) system, cause theone or more processors to: cause a first light source to pump at leastone qubit ion from a first manifold of a first plurality of manifolds toa second manifold of the first plurality of manifolds; cause a secondlight source to drive the at least one qubit ion via a partial clocktransition from the second manifold of the first plurality of manifoldsto a third manifold of a second plurality of manifolds; cause a thirdlight source to apply one or more Raman pulses to transfer the at leastone qubit ion from the third manifold of the second plurality ofmanifolds to a fourth manifold of the second plurality of manifolds;cause a fourth light source to flush the at least one qubit ion using ahigh-fidelity pumping back to the first plurality of manifolds; andcause a fifth light source to illuminate the first plurality ofmanifolds for verification.
 9. The non-transitory computer readablemedium of claim 8, wherein the instructions for flushing the at leastone qubit ion comprises instructions for: pumping the at least one qubition from the third manifold of the second plurality of manifolds to thesecond manifold of the first plurality of manifolds; and pumping the atleast one qubit ion from the second manifold of the first plurality ofmanifolds to the first manifold of the first plurality of manifolds. 10.The non-transitory computer readable medium of claim 9, furthercomprising instructions for repeating the flushing the at least onequbit ion.
 11. The non-transitory computer readable medium of claim 8,wherein: the first plurality of manifolds is associated with a S_(1/2)manifold; and the second plurality of manifolds is associated with aD_(5/2) manifold.
 12. The non-transitory computer readable medium ofclaim 8, further comprising instructions for applying one or moreadditional Raman pulses to initialize one or more qubit ions of the atleast one qubit ion that failed to initialize during the application ofthe one or more Raman pulses.
 13. The non-transitory computer readablemedium of claim 8, further comprising instructions for, prior to pumpingthe at least one qubit from the first manifold or after illuminating thefirst plurality of manifolds: applying one or more second Raman pulsesto transfer at least one ancilla ion from the fourth manifold of thesecond plurality of manifolds to the third manifold of the secondplurality of manifolds; transferring the at least one ancilla ion fromthe third manifold of the second plurality of manifolds to the secondmanifold of the first plurality of manifolds; and applying one or moreof an individual Raman beam or a global beam to separate the at leastone ancilla ion from the at least one qubit ion.
 14. The non-transitorycomputer readable medium of claim 13, further comprising instructionsfor, prior to applying the one or more second Raman pulses, pumping atleast one coolant ion from the second manifold of the first plurality ofmanifolds to the first manifold of the first plurality of manifolds. 15.A quantum information processing (QIP) system, comprising: a laserscheme including a plurality of light sources and configured to apply atleast one of the plurality of light sources to a plurality of ions inthe QIP system; and a controller configured to execute instructions in amemory to: cause a first light source of the plurality of light sourcesto pump at least one qubit ion from a first manifold of a firstplurality of manifolds to a second manifold of the first plurality ofmanifolds; cause a second light source of the plurality of light sourcesto drive the at least one qubit ion via a partial clock transition fromthe second manifold of the first plurality of manifolds to a thirdmanifold of a second plurality of manifolds; cause a third light sourceof the plurality of light sources to apply one or more Raman pulses totransfer the at least one qubit ion from the third manifold of thesecond plurality of manifolds to a fourth manifold of the secondplurality of manifolds; cause a fourth light source of the plurality oflight sources to flush the at least one qubit ion using a high-fidelitypumping back to the first plurality of manifolds; and cause a fifthlight source of the plurality of light sources to illuminate the firstplurality of manifolds for verification.
 16. The QIP system of claim 15,wherein the controller is further configured to: pump the at least onequbit ion from the third manifold of the second plurality of manifoldsto the second manifold of the first plurality of manifolds; and pump theat least one qubit ion from the second manifold of the first pluralityof manifolds to the first manifold of the first plurality of manifolds.17. The QIP system of claim 15, wherein: the first plurality ofmanifolds is associated with a S_(1/2) manifold; and the secondplurality of manifolds is associated with a D_(5/2) manifold.
 18. TheQIP system of claim 15, wherein the controller is further configured toapply one or more additional Raman pulses to initialize one or morequbit ions of the at least one qubit ion that failed to initializeduring the application of the one or more Raman pulses.
 19. The QIPsystem of claim 15, wherein the controller is further configured to,prior to pumping the at least one qubit from the first manifold or afterilluminating the first plurality of manifolds: apply one or more secondRaman pulses to transfer at least one ancilla ion from the fourthmanifold of the second plurality of manifolds to the third manifold ofthe second plurality of manifolds; transfer the at least one ancilla ionfrom the third manifold of the second plurality of manifolds to thesecond manifold of the first plurality of manifolds; and apply one ormore of an individual Raman beam or a global beam to separate the atleast one ancilla ion from the at least one qubit ion.
 20. The QIPsystem of claim 19, wherein the controller is further configured to,prior to applying the one or more second Raman pulses, pump at least onecoolant ion from the second manifold of the first plurality of manifoldsto the first manifold of the first plurality of manifolds.